QM Interpretations as applied to QFT

[charters]

[Moderator's Note: Thread spun off from previous discussion.]

I didn't say that retrocausal theories can't get out the statistics, I said they aren't generalized to QFT fully, neither is the TSVF you are discussing. Kastner's work can be considered to have shown that it might be able to replicate aspects of QED, but I'm not aware of a full proof that it works in the QFT case.

Many Worlds has many issues with QFT, such as the absence of pure states for finite volume systems. And the Born rule has never been proven to hold

MWI and the TSVF are both easily generalized to QFT. One only needs to define the decoherence basis for the fields (see https://arxiv.org/abs/quant-ph/9510021) and then one simply interprets the decoherent histories as ontological worlds. The advantage of the TSVF is having a simple way of introducing the Born Rule as an axiom, ie placing the future boundary to prefer one decoherent history through a Born weighted random choice makes the "chosen/real" world overwhelmingly likely to have typical quantum statistics.

The Reeh Schlieder/Von Neumann Type 3 issue you allude to is also not really a problem for these interpretations. Rather, this is an issue for Copenhageners who want to represent measurement by projection operators on local algebras. There are no local projections at all in MWI or TSVF.

 

[DarMM]

One only needs to define the decoherence basis for the fields (see https://arxiv.org/abs/quant-ph/9510021) and then one simply interprets the decoherent histories as ontological worlds

To define decoherence you need the Born rule. There's no non-circular proof of the Born rule in MWI. I don't know how many I've read at this point (Wallace's, Carroll's, Araújo's, DeWitt's, Zurek's,...), they are all different and all have a point of circularity.

For TSVF you'd need to show that the renormalizations required for two Schrödinger picture states are valid. The Schrödinger picture requires additional renormalizations not present in the Heisenberg picture, the TSVF would require even more since it has two boundary hypersurfaces. I've never seen this demonstrated. And that would just be the beginning of transferring it to QFT.

The Reeh Schlieder/Von Neumann Type 3 issue you allude to is also not really a problem for these interpretations

It is a problem for Many Worlds because it requires you to accept that the ontological state for any system occupying a finite volume is a density matrix. Since density matrices involve classical probability it requires you to say that classical ignorance is "real" in some sense.
I've never seen a clear account of what this "density-matrix realism" is supposed to mean, though Timpson and Wallace have attempted to do so. Timpson switched to QBism shortly afterward so little else has come of it.

Rather, this is an issue for Copenhageners who want to represent measurement by projection operators on local algebras

I've never heard of this. Haag and Araki who developed the formalism of AQFT and identified the presence of Type III algebras were (Neo-)Copenhagenists. I've never read anything about needing a projection operator.

 

[charters]

To define decoherence you need the Born rule

This is just not true. Here is a good recent intro to decoherence: https://arxiv.org/abs/1811.09062. Decoherence concerns only unitary evolution and the derivation of the preferred basis, not getting outcomes, which is when the Born rule arises.

For TSVF you'd need to show that the renormalizations required for two Schrödinger picture states are valid.

Never heard this before. Is there a source for this argument or is it only your own? I do not at all see why the boundary conditions, either initial or final, need to be narrowly restricted to the Schrödinger picture. A two-time interpretation is just as sensible and meaningful in a path integral or Heisenberg picture.

It is a problem for Many Worlds because it requires you to accept that the ontological state for any system occupying a finite volume is a density matrix. Since density matrices involve classical probability it requires you to say that classical ignorance is "real" in some sense.

This is always true in MWI or any realist/representational interpretation that doesn't have classically defined hidden variables. Nothing about it is exacerbated by QFT in particular.

I've never heard of this. Haag and Araki who developed the formalism of AQFT and identified the presence of Type III algebras were (Neo-)Copenhagenists. I've never read anything about needing a projection operator.

See section 4 https://arxiv.org/abs/quant-ph/0001107. The entire issue with Type 3 is the inability to disentangle subsystems via projection. This is also irrelevant to MWI, TSVF, or any other interpretation, insofar as we have a UV cutoff QFT, like in the SM/anything realistic, which are Type 1.

Timpson switched to QBism shortly afterward

Source?

 

[DarMM]

I'll discuss any of these issues on another thread. There's three lines of discussion here.

1. Does decoherence need the Born rule. My view is that it does as I don't think Quantum Darwinism managed to provide a Born rule free derivation. Standard derivations of decoherence do use the Born rule, essentially by assuming the use of the tracing operation. I've read your reference before so we can base it on that and refutations by Ruth Kastner
2. The validity of the TSVF as a complete realist retrocausal account of QFT
3. Does Copenhagen require projections. I've read Clifton and Halvorson's paper before but I'm not sure what aspect presents problems for Copenhagen there. Maybe specific forms of Copenhagen require them

If you want to discuss them somewhere else I'd be happy to.

Nothing about it is exacerbated by QFT in particular.

QFT has the Type-III factors that force finite volume states to be mixed.

As for Timpson, I don't have a scientific reference that he changed his mind, he just seems to advocate QBism in recent talks such as this where he is actually debating against a Many Worlds proponent:
https://iai.tv/video/is-reality-an-illusion